src/FOL/FOL_lemmas1.ML
changeset 9264 051592f4236a
parent 7422 c63d619286a3
--- a/src/FOL/FOL_lemmas1.ML	Thu Jul 06 13:11:32 2000 +0200
+++ b/src/FOL/FOL_lemmas1.ML	Thu Jul 06 13:28:36 2000 +0200
@@ -12,39 +12,40 @@
 
 (*** Classical introduction rules for | and EX ***)
 
-qed_goal "disjCI" (the_context ()) 
-   "(~Q ==> P) ==> P|Q"
- (fn prems=>
-  [ (rtac classical 1),
-    (REPEAT (ares_tac (prems@[disjI1,notI]) 1)),
-    (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);
+val prems = Goal "(~Q ==> P) ==> P|Q";
+by (rtac classical 1);
+by (REPEAT (ares_tac (prems@[disjI1,notI]) 1));
+by (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ;
+qed "disjCI";
 
 (*introduction rule involving only EX*)
-qed_goal "ex_classical" (the_context ()) 
-   "( ~(EX x. P(x)) ==> P(a)) ==> EX x. P(x)"
- (fn prems=>
-  [ (rtac classical 1),
-    (eresolve_tac (prems RL [exI]) 1) ]);
+val prems = Goal "( ~(EX x. P(x)) ==> P(a)) ==> EX x. P(x)";
+by (rtac classical 1);
+by (eresolve_tac (prems RL [exI]) 1) ;
+qed "ex_classical";
 
 (*version of above, simplifying ~EX to ALL~ *)
-qed_goal "exCI" (the_context ()) 
-   "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)"
- (fn [prem]=>
-  [ (rtac ex_classical 1),
-    (resolve_tac [notI RS allI RS prem] 1),
-    (etac notE 1),
-    (etac exI 1) ]);
+val [prem]= Goal "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)";
+by (rtac ex_classical 1);
+by (resolve_tac [notI RS allI RS prem] 1);
+by (etac notE 1);
+by (etac exI 1) ;
+qed "exCI";
 
-qed_goal "excluded_middle" (the_context ()) "~P | P"
- (fn _=> [ rtac disjCI 1, assume_tac 1 ]);
+Goal"~P | P";
+by (rtac disjCI 1);
+by (assume_tac 1) ;
+qed "excluded_middle";
 
 (*For disjunctive case analysis*)
 fun excluded_middle_tac sP =
     res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
 
-qed_goal "case_split_thm" (the_context ()) "[| P ==> Q; ~P ==> Q |] ==> Q"
-  (fn [p1,p2] => [rtac (excluded_middle RS disjE) 1,
-                  etac p2 1, etac p1 1]);
+val [p1,p2] = Goal"[| P ==> Q; ~P ==> Q |] ==> Q";
+by (rtac (excluded_middle RS disjE) 1);
+by (etac p2 1);
+by (etac p1 1);
+qed "case_split_thm";
 
 (*HOL's more natural case analysis tactic*)
 fun case_tac a = res_inst_tac [("P",a)] case_split_thm;
@@ -54,39 +55,41 @@
 
 
 (*Classical implies (-->) elimination. *)
-qed_goal "impCE" (the_context ()) 
-    "[| P-->Q;  ~P ==> R;  Q ==> R |] ==> R"
- (fn major::prems=>
-  [ (resolve_tac [excluded_middle RS disjE] 1),
-    (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]);
+val major::prems = Goal "[| P-->Q;  ~P ==> R;  Q ==> R |] ==> R";
+by (resolve_tac [excluded_middle RS disjE] 1);
+by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ;
+qed "impCE";
 
 (*This version of --> elimination works on Q before P.  It works best for
   those cases in which P holds "almost everywhere".  Can't install as
   default: would break old proofs.*)
-qed_goal "impCE'" (the_context ()) 
-    "[| P-->Q;  Q ==> R;  ~P ==> R |] ==> R"
- (fn major::prems=>
-  [ (resolve_tac [excluded_middle RS disjE] 1),
-    (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]);
+val major::prems = Goal "[| P-->Q;  Q ==> R;  ~P ==> R |] ==> R";
+by (resolve_tac [excluded_middle RS disjE] 1);
+by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ;
+qed "impCE'";
 
 (*Double negation law*)
-qed_goal "notnotD" (the_context ()) "~~P ==> P"
- (fn [major]=>
-  [ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]);
+Goal"~~P ==> P";
+by (rtac classical 1);
+by (etac notE 1);
+by (assume_tac 1);
+qed "notnotD";
 
-qed_goal "contrapos2" (the_context ()) "[| Q; ~ P ==> ~ Q |] ==> P" (fn [p1,p2] => [
-        rtac classical 1,
-        dtac p2 1,
-        etac notE 1,
-        rtac p1 1]);
+val [p1,p2] = Goal"[| Q; ~ P ==> ~ Q |] ==> P";
+by (rtac classical 1);
+by (dtac p2 1);
+by (etac notE 1);
+by (rtac p1 1);
+qed "contrapos2";
 
 (*** Tactics for implication and contradiction ***)
 
 (*Classical <-> elimination.  Proof substitutes P=Q in 
     ~P ==> ~Q    and    P ==> Q  *)
-qed_goalw "iffCE" (the_context ()) [iff_def]
-    "[| P<->Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R"
- (fn prems =>
-  [ (rtac conjE 1),
-    (REPEAT (DEPTH_SOLVE_1 
-        (etac impCE 1  ORELSE  mp_tac 1  ORELSE  ares_tac prems 1))) ]);
+val major::prems = 
+Goalw  [iff_def] "[| P<->Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R";
+by (rtac (major RS conjE) 1);
+by (REPEAT_FIRST (etac impCE));
+by (REPEAT (DEPTH_SOLVE_1 (mp_tac 1  ORELSE  ares_tac prems 1)));
+qed "iffCE";
+